SOLUTION: how do i put this problem together if 4 is added to the square of a composite integer the result is 5 less than 10 times that integer.find the integer

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Question 244639: how do i put this problem together if 4 is added to the square of a composite integer the result is 5 less than 10 times that integer.find the integer
Found 2 solutions by solver91311, JimboP1977:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the integer.

4 added to the square of the integer:

5 less than 10 times the integer:

The two quantities are equal because the questions says "the result is," so

Rearrange to standard form, then solve the quadratic. Hint: It factors. You will get two roots, only one of which is a composite integer. Discard the root that is not a composite integer and the remaining root is your answer.

John

Answer by JimboP1977(311) (Show Source):
You can put this solution on YOUR website!
4+x^2 = 10x-5
x^2-10x+9=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=64 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9, 1. Here's your graph:

As the integer is a composite number ie can be divide by a number other than 1 and itself, the answer must be 9